Question

Determine whether the statement is always, sometimes, or never true. Lines AB, CD, and EF determine plan P. If GH intersects AB, then GH lies on plan P.

Answer 1

Answer:  sometimes true

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Explanation:

The plane P can be thought of a perfectly flat ground. Now imagine a flag pole which represents line GH. If AB is drawn in chalk on the pavement, and this line AB intersects the base of the flagpole, then we've made AB and GH intersect. However, this example shows that GH is not on the plane P.

Is it possible to have GH be in the the plane? Yes. We could easily draw another chalk line on the ground to have it intersect AB somewhere. But as the previous paragraph says, it's also possible that GH is not in the plane.

Therefore, the statement is sometimes true